Let x and y be number of A and B products.
∴According to the question,
0.5x + y ≤ 40, 200x + 300y ≥ 10000, x ≥ 14, y ≥ 16
Maximize Z = 20x + 30y
The feasible region determined by 0.5x + y ≤ 40, 200x + 300y ≥ 10000, x ≥ 14, y ≥ 16 is given by
The corner points of feasible region are A(14,33) , B(14,24) , C(26,16), D(48,16).
The value of Z at corner points are
Corner Point |
Z = 20x + 30y |
|
A(14, 33) |
1270 |
|
B(14, 24) |
1000 |
|
C(26, 16) |
1000 |
|
D(48, 16) |
1440 |
Maximum |
The maximum value of Z is 1440 at point (48,16).
Hence, the manufacturer should manufacture 48 A products and 16 B products to maximize their profit of Rs.1440.